[% LAST %] is not the same as loop.last().

The data you've shown is a little too messy for me (to try to fix it up to actually match its usage in the given template...), but the general idea would be something like this:

my $data = {
    employee => [
                    { name => 'Foo'  },
                    { name => 'Bar'  },
                    { name => 'Baz'  },
                ]
};

my $template = Template->new();
$template->process(\*DATA, $data)
    || die "Template process failed: ", $template->error(), "\n";

__DATA__
[% FOREACH person IN employee %]
    [%- IF loop.index() %][% loop.size()>2 && loop.last() ? ' or':',' 
+%] [% END %]
    [%- person.name %]
[%- END %].
[download]

Output:

Foo, Bar or Baz.
[download]